Mehmet Ertugrul Çelebi

Analysis of input-output clustering for determining centers of RBFN

The key point in design of radial basis function networks is to specify the number and the locations of the centers. Several heuristic hybrid learning methods, which apply a clustering algorithm for locating the centers and subsequently a linear leastsquares method for the linear weights, have been previously suggested. These hybrid methods can be put into two groups, which will be called as input clustering (IC) and input-output clustering (IOC), depending on whether the output vector is also involved in the clustering process. The idea of concatenating the output vector to the input vector in the clustering process has independently been proposed by several papers in the literature although none of them presented a theoretical analysis on such procedures, but rather demonstrated their effectiveness in several applications. The main contribution of this paper is to present an approach for investigating the relationship between clustering process on input-output training samples and the mean squared output error in the context of a radial basis function netowork (RBFN). We may summarize our investigations in that matter as follows: 1) A weighted mean squared input-output quantization error, which is to be minimized by IOC, yields an upper bound to the mean squared output error. 2) This upper bound and consequently the output error can be made arbitrarily small (zero in the limit case) by decreasing the quantization error which can be accomplished through increasing the number of hidden units.

Full rate full diversity space-time block code selection for more than two transmit antennas

In this paper, we propose a full rate space-time block code selection technique, which achieves full diversity when more than two transmit antennas are used for transmission. Only one or few feedback bits are needed at the transmitter, representing relative state information of the channels. Moreover, the proposed scheme allows separate decoding of transmitted symbols at the receiver. It is shown by computer simulations that, the new approach provides SNR improvement, especially when feedback errors occur, compared to the transmit antenna selection technique associated with Alamoutis scheme, for the same number of feedback bits

Increasing Diversity with Feedback: Balanced Space-Time Block Coding

We propose a novel coding scheme, which guarantees full diversity for any number of transmit antennas, provided that few bits of feedback from the receiver to the transmitter are available. This coding scheme is arranged as an extension of orthogonal space-time block coding and preserves its linear decoding complexity. Moreover, it is full rate when the underlying coding method is the Alamoutis scheme. It is shown by computer simulations that the new approach provides SNR improvement, and it is more resilient to feedback errors compared to the antenna selection technique on the basis of same number of feedback bits.

Diversity Enhancement with Cooperative Balanced Space-Time Block Coding

In this paper, a balanced space-time block coding method for cooperative relay networks is proposed which guarantees full diversity for any number of mobile relays with minimal delay, provided that few bits of feedback from the destination to the source and the relays are available. As in the case of orthogonal space-time block codes, all transmitted symbols are separately decoded both in the relays and the destination. Therefore, decoding complexity is linear. Many of the proposed solutions in the literature are distributed space-time codes which are designed for limited number of relays. In the proposed scheme, as many number of relays as necessary can be included to increase diversity. Moreover, the proposed scheme has better signal-to-noise ratio improvement compared to relay selection schemes. Lastly, the new method satisfies power consumption fairness among relay terminals and requires no knowledge of topology information.

Folded tree maximum-likelihood decoder for Kronecker product-based codes

In this paper, we propose efficient maximum-likelihood (ML) decoding for binary Kronecker product-based (KPB) codes. This class of codes, have a matrix defined by the n-fold iterated Kronecker product Gn = F⊗n of a binary upper-triangular kernel matrix F, where some columns are suppressed given a specific puncturing pattern. Polar and Reed- Muller codes are well known examples of such KPB codes. The triangular structure of Gn enables to perform ML decoding as a binary tree search for the closest codeword to the received point. We take advantage of the highly regular fractal structure of Gn and the “tree folding” technique to design an efficient ML decoder, enabling to decode relatively longer block lengths than with a standard binary tree search. The tree κ-folding operation transforms the binary tree with N levels into a non-binary tree with N=2κ levels, where the search can be significantly accelerated by a suitable ordering of the branch metrics. For a given κ we can find (n over κ) different folding which lead to decoders with different complexity, for a given code. Using the proposed folded tree decoder, we provide exact ML performances of some Reed-Muller and polar codes over a binary AWGN channel for the block length up to 256.

Extended Cooperative Balanced Space-Time Block Coding for Increased Efficiency in Wireless Sensor Networks

Diversity techniques for communications among sensors are very effective tool to increase reception quality and battery lifetimes. A well-known method to increase diversity in cooperative communications is sensor (relay) selection. However, sensor selection method may lead to the selection of the same (near) sensor for transmission over a long period. One of the alternative techniques to sensor selection is cooperative balanced space-time block coding which utilizes every sensor in sight, thus, distributes the energy consumption among many sensors. Furthermore, it guarantees full diversity for any number of relay sensors. In this work, we consider dual-hop amplify-and-forward wireless sensor network and extend the cooperative balanced space-time block code family to improve its performance. In the proposed scheme, a larger number of codes can be generated for improved coding gain, and better signal-to-noise ratio improvement can be obtained compared to sensor selection schemes.

Robust locally optimal filters: Kalman and Bayesian estimation theory

This paper presents a unified approach to local optimality, robustness, and Bayesian estimation theory concepts in deriving Kalman filtering equations in the case of non-Gaussian observation noise. In most of these derivations, an approximation criterion proposed by Masreliez is used: the prediction error density is approximately Gaussian. It is shown that locally optimal Kalman filters are equivalent to one-step MAP iterative procedures. The introduction of nonlinear iterative techniques adds a new dimension to the analysis of recursive non-Gaussian estimation. Moreover, to estimate the parameters of the Kalman model, a direct solution of MAP equations is obtained through an m-interval piecewise linear approximation (MIPLA) of the locally optimal nonlinearity (score function). Robustness is achieved by proper modification and approximation of the score function. Finally, the performance of the filters in question are tested under intensive Monte Carlo simulations. Satisfactory results are obtained even in the case of extremely impulsive observation noise (Cauchy contaminated Gaussian).

Outage probability analysis of cooperative spatial modulation systems

The capacity analysis of the spatial modulation (SM) scheme is different than that of the multiple-input multiple-output (MIMO) systems. Since the information is conveyed not only through the M-ary constellation domain but also through the antenna domain, the capacity of SM is expressed as the sum of the capacities of these two domains. Due to this summation, the outage probability of SM differs from the conventional systems. A detailed analysis of the outage probability of SM has not been given in the literature yet. In this work, first, we derive the outage probability performance of the classical SM system and second, we extend the results to the cooperative scenarios under fixed, selective and incremental relaying techniques. It is shown that SM and cooperative SM systems provide better performance compared to conventional modulation systems in terms of outage probability.

Folded successive cancelation decoding of polar codes

Polar codes are the first explicit class of codes that are provably capacity-achieving under the successive cancelation (SC) decoding. As a suboptimal decoder, SC has quasi-linear complexity N(1 + log N) in the code length N. In this paper, we propose a new non-binary SC decoder with reduced complexity N/2(1 + log N/2) based on the folding operation, which was first proposed in [11] to implement folded tree maximum-likelihood decoding of polar codes. Simulation results for the additive white Gaussian noise channel show that folded SC decoders can achieve the same error performance of standard SC by suitable selecting the folding of the polar code.

Multiple Folding for Successive Cancelation Decoding of Polar Codes

Polar coding is known as the first provably capacity-achieving coding scheme under low-complexity suboptimal successive cancelation decoding (SCD). The large error-correction capability of finite-length polar codes is mostly achieved with relatively long codes. SCD is the conventional decoder for polar codes and exhibits a quasi-linear complexity in terms of the code length. Practical decoder schemes with low latency are important for high-speed polar coding applications. In this letter, we propose a nonbinary multiple folded SCD scheme to reduce the decoding latency of standard binary polar codes. Multiple foldings were first proposed to improve the efficiency of folded tree maximum-likelihood decoder for Kronecker product-based codes. By successively applying the folding operation κ times on the SCD, for a code length N, the latency is reduced from 2N - 1 to (N/2κ-1) - 1 time slots, assuming full parallelization. We show that multiple folded SCD can be effectively implemented for up to κ = 3 foldings due to memory limitations. This decoder achieves exactly the same performance of the original SCD with significantly reduced latency.